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/* Copyright 2015 The Chromium OS Authors. All rights reserved.
* Use of this source code is governed by a BSD-style license that can be
* found in the LICENSE file.
*/
#include "common.h"
#include "mat33.h"
#include "math.h"
#include "util.h"
#define K_EPSILON 1E-5f
void mat33_fp_init_zero(mat33_fp_t A)
{
memset(A, 0, sizeof(mat33_fp_t));
}
void mat33_fp_init_diagonal(mat33_fp_t A, fp_t x)
{
const size_t N = 3;
size_t i;
mat33_fp_init_zero(A);
for (i = 0; i < N; ++i)
A[i][i] = x;
}
void mat33_fp_scalar_mul(mat33_fp_t A, fp_t c)
{
const size_t N = 3;
size_t i;
for (i = 0; i < N; ++i) {
size_t j;
for (j = 0; j < N; ++j)
A[i][j] = fp_mul(A[i][j], c);
}
}
void mat33_fp_swap_rows(mat33_fp_t A, const size_t i, const size_t j)
{
const size_t N = 3;
size_t k;
if (i == j)
return;
for (k = 0; k < N; ++k) {
fp_t tmp = A[i][k];
A[i][k] = A[j][k];
A[j][k] = tmp;
}
}
/*
* Returns the eigenvalues and corresponding eigenvectors of the _symmetric_
* matrix.
* The i-th eigenvalue corresponds to the eigenvector in the i-th _row_ of
* "eigenvecs".
*/
void mat33_fp_get_eigenbasis(mat33_fp_t S, fpv3_t e_vals,
mat33_fp_t e_vecs)
{
const size_t N = 3;
sizev3_t ind;
size_t i, j, k, l, m;
for (k = 0; k < N; ++k) {
ind[k] = mat33_fp_maxind(S, k);
e_vals[k] = S[k][k];
}
mat33_fp_init_diagonal(e_vecs, FLOAT_TO_FP(1.0f));
for (;;) {
fp_t y, t, s, c, p, sum;
m = 0;
for (k = 1; k + 1 < N; ++k)
if (fp_abs(S[k][ind[k]]) > fp_abs(S[m][ind[m]]))
m = k;
k = m;
l = ind[m];
p = S[k][l];
/*
* Note: K_EPSILON(1E-5) is too small to fit into 32-bit
* fixed-point(with 16 fp bits). The minimum positive value is
* 1 which is approximately 1.52E-5, so the
* FLOAT_TO_FP(K_EPSILON) becomes zero.
*/
if (fp_abs(p) <= FLOAT_TO_FP(K_EPSILON))
break;
y = fp_mul(e_vals[l] - e_vals[k], FLOAT_TO_FP(0.5f));
t = fp_abs(y) + fp_sqrtf(fp_sq(p) + fp_sq(y));
s = fp_sqrtf(fp_sq(p) + fp_sq(t));
c = fp_div_dbz(t, s);
s = fp_div_dbz(p, s);
t = fp_div_dbz(fp_sq(p), t);
if (y < FLOAT_TO_FP(0.0f)) {
s = -s;
t = -t;
}
S[k][l] = FLOAT_TO_FP(0.0f);
e_vals[k] -= t;
e_vals[l] += t;
for (i = 0; i < k; ++i)
mat33_fp_rotate(S, c, s, i, k, i, l);
for (i = k + 1; i < l; ++i)
mat33_fp_rotate(S, c, s, k, i, i, l);
for (i = l + 1; i < N; ++i)
mat33_fp_rotate(S, c, s, k, i, l, i);
for (i = 0; i < N; ++i) {
fp_t tmp = fp_mul(c, e_vecs[k][i]) -
fp_mul(s, e_vecs[l][i]);
e_vecs[l][i] = fp_mul(s, e_vecs[k][i]) +
fp_mul(c, e_vecs[l][i]);
e_vecs[k][i] = tmp;
}
ind[k] = mat33_fp_maxind(S, k);
ind[l] = mat33_fp_maxind(S, l);
sum = FLOAT_TO_FP(0.0f);
for (i = 0; i < N; ++i)
for (j = i + 1; j < N; ++j)
sum += fp_abs(S[i][j]);
/*
* Note: K_EPSILON(1E-5) is too small to fit into 32-bit
* fixed-point(with 16 fp bits). The minimum positive value is
* 1 which is approximately 1.52E-5, so the
* FLOAT_TO_FP(K_EPSILON) becomes zero.
*/
if (sum <= FLOAT_TO_FP(K_EPSILON))
break;
}
for (k = 0; k < N; ++k) {
m = k;
for (l = k + 1; l < N; ++l)
if (e_vals[l] > e_vals[m])
m = l;
if (k != m) {
fp_t tmp = e_vals[k];
e_vals[k] = e_vals[m];
e_vals[m] = tmp;
mat33_fp_swap_rows(e_vecs, k, m);
}
}
}
/* index of largest off-diagonal element in row k */
size_t mat33_fp_maxind(mat33_fp_t A, size_t k)
{
const size_t N = 3;
size_t i, m = k + 1;
for (i = k + 2; i < N; ++i)
if (fp_abs(A[k][i]) > fp_abs(A[k][m]))
m = i;
return m;
}
void mat33_fp_rotate(mat33_fp_t A, fp_t c, fp_t s,
size_t k, size_t l, size_t i, size_t j)
{
fp_t tmp = fp_mul(c, A[k][l]) - fp_mul(s, A[i][j]);
A[i][j] = fp_mul(s, A[k][l]) + fp_mul(c, A[i][j]);
A[k][l] = tmp;
}
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